Tacita Dean's Film in the Turbine Hall at Tate Modern. Photograph: Ray Tang/Rex Features

The Turbine Hall of Tate Modern is plunged into deep black gloom. At its east end, like the stained glass window of a cathedral, is a giant vertical screen. It is framed at the edges with sprocket holes, so we feel we are looking at a vast reel of film. In the centre, an ever-changing series of images: a snail on a wind-wobbled leaf, the powerful spume of a fountain, a chimney loosing trails of vapour. Sometimes the image is of the back wall of the Turbine Hall itself, but with its gridded form coloured in red, yellow and blue so it resembles a Mondrian. Or with a giant egg apparently floating from ceiling to floor.

This is the British artist Tacita Dean's offering for the most prestigious art commission in the land, Tate Modern's Unilever series. The 12th artist to be invited to occupy the cavernous space, she follows in the footsteps of figures including Juan Muñoz, Bruce Naumann, Olafur Eliasson and Doris Salcedo. According to the Tate Modern director, Chris Dercon, 26 million people have now seen these works since the series began in 2000 with Louise Bourgeois.

Her work, said Dean, is both an act of mourning and an argument for the future. Simply called Film, it is shot on 35mm and painstakingly edited by her and her alone. It is a homage to a form that is about to die, killed off by digital film-making, unless fast action is taken. "This beautiful medium, which we invented 125 years ago, is about to go," she said. "How long have we got? I hope we've got a year left. It's that critical." Laboratories that are capable of printing film are "in single figures in the world", she said. The continued manufacture of film is also in doubt.

Film is, in part, a showcase of what 35mm can do, she said: its very limitations meaning the artist must invent and improvise. To create her "special effects" – such as a vast circular aperture containing a winking eye apparently appearing out of the Tate Modern back wall – she used old-fashioned techniques from cinema's early days, such as glass matte painting, masking and double exposure. The language of analogue film-making, said Dean, was as important to her as a painter's canvas and paint. When it goes, she said, "I might go back to oil painting. Or write a novel."

Even so, she said, she is "not a Luddite", nor is she "fetishising the medium". "I am in no way anti-digital," she said. "I want to make that perfectly clear. But I love film and I don't want to lose my ability to make it and I think I probably will." The major differences between film and digital were in the making, she said. "Digital relies on post-production. No longer do you rely on the moment; and you lose a certain vitality of the moment."

Dean, 45, who was born in Kent and is based in Berlin, is known for her serious-minded, beautiful, patiently paced films – including portraits of artistic figures such as the late painter Cy Twombly, and the late choreographer Merce Cunningham. Of being asked to occupy the Turbine Hall, she said: "I am not known for making works on a spectacular scale, so I had to go somewhere I had never been before. The Turbine Hall commission is about the spectacular: there is no getting away from that. So I thought, I'm going to do something spectacular – not a 148-minute film about an old man."

The very making of Film reflected, said Dean, the fact of the medium's crisis. Due to a loss of skills in the Dutch laboratory she used there was a serious error in the way the film was cut that transpired a week and a half ago. The mistake would have resulted in white flashes being seen between each shot when the film was shown. "We've been through the valley of the shadow of death," said Dean of the disaster.

Film was saved by Steve Farman, of the Tonbridge-based company Professional Negative Cutting. He drove to Amsterdam, recut the film with Dean, and drove through the night to deliver it to the Tate curator, Nicholas Cullinan, in the early hours of Saturday morning. Farman, 52, said helping out on the project had been "the crowning glory of my career" – easily trumping work on Troy and Batman Begins. He said: "I am the last person doing it in the UK now. It's very sad, it used to be 200 people, but it's a dying art. When I pack up, that will be it."

Tacita Dean's Film is at Tate Modern, London SE1, from 11 October until 11 March.